Answer Happy

I made a few fake decks of cards to help make it look like I’m
good at magic tricks. One deck is entirely the seven of spades
(hereafter referred to as the “Seven of Spades Deck”). One deck is
half seven of spades and half four of hearts (hereafter referred to
as the “Half and Half Deck”). One deck has thirty-nine cards that
are seven of spades and thirteen that are four of hearts (hereafter
referred to as the “Mostly Spades Deck”). And one is a normal deck
of cards that I show my audience and try to convince that the other
decks of cards are probably normal as well and they certainly don’t
need to check for themselves.
(a) I have an audience member select one of the decks of
cards (after I’ve mixed them up), open it, and select a card.
Shockingly, she selected the seven of spades. What is the
probability that they selected each of the four decks?
(b) Now I have four volunteers come up on stage (one wife, one
daughter, and two dogs. The stage is anything that’s “not sitting
on the couch.”) We pick a deck at random and have each of them take
a card. They each take a seven of spades. What's the probability
that the deck chosen was the Seven of Spades Deck?
(c) Suppose instead that one of them chose a seven of spades and
the other three chose a four of hearts. What’s the probability that
they selected each of the four decks?